message stringlengths 2 67k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 463 109k | cluster float64 19 19 | __index_level_0__ int64 926 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Two players play a simple game. Each player is provided with a box with balls. First player's box contains exactly n1 balls and second player's box contains exactly n2 balls. In one move first player can take from 1 to k1 balls from his box and throw them away. Similarly, the second player can take from 1 to k2 balls from his box in his move. Players alternate turns and the first player starts the game. The one who can't make a move loses. Your task is to determine who wins if both players play optimally.
Input
The first line contains four integers n1, n2, k1, k2. All numbers in the input are from 1 to 50.
This problem doesn't have subproblems. You will get 3 points for the correct submission.
Output
Output "First" if the first player wins and "Second" otherwise.
Examples
Input
2 2 1 2
Output
Second
Input
2 1 1 1
Output
First
Note
Consider the first sample test. Each player has a box with 2 balls. The first player draws a single ball from his box in one move and the second player can either take 1 or 2 balls from his box in one move. No matter how the first player acts, the second player can always win if he plays wisely.
Submitted Solution:
```
a, b, c, d = map(int,input().split())
if a > b:
print('First')
elif a < b:
print("Second")
else:
if c > d:
print('First')
elif d > c:
print("Second")
``` | instruction | 0 | 58,432 | 19 | 116,864 |
No | output | 1 | 58,432 | 19 | 116,865 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Two players play a simple game. Each player is provided with a box with balls. First player's box contains exactly n1 balls and second player's box contains exactly n2 balls. In one move first player can take from 1 to k1 balls from his box and throw them away. Similarly, the second player can take from 1 to k2 balls from his box in his move. Players alternate turns and the first player starts the game. The one who can't make a move loses. Your task is to determine who wins if both players play optimally.
Input
The first line contains four integers n1, n2, k1, k2. All numbers in the input are from 1 to 50.
This problem doesn't have subproblems. You will get 3 points for the correct submission.
Output
Output "First" if the first player wins and "Second" otherwise.
Examples
Input
2 2 1 2
Output
Second
Input
2 1 1 1
Output
First
Note
Consider the first sample test. Each player has a box with 2 balls. The first player draws a single ball from his box in one move and the second player can either take 1 or 2 balls from his box in one move. No matter how the first player acts, the second player can always win if he plays wisely.
Submitted Solution:
```
n1, n2, k1, k2 = map(int, input().split())
c = 0
c2 = 0
while k1 != 0 and n1 != 0: #n1 = 5, n2 = 7, k1 = 3, k2 = 5
n1 -= 1
c += 1
k1 -= 1
while k2 != 0 and n2 != 0:
n2 -= 1
c2 += 1
k2 -= 1
if c < c2:
print('Second')
else:
print('First')
``` | instruction | 0 | 58,433 | 19 | 116,866 |
No | output | 1 | 58,433 | 19 | 116,867 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose.
Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability.
Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win.
Input
The only string contains the string s of length l (3 β€ l β€ 5000), consisting of small English letters only.
Output
Print the only number β the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>
Examples
Input
technocup
Output
1.000000000000000
Input
tictictactac
Output
0.333333333333333
Input
bbaabaabbb
Output
0.100000000000000
Note
In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely.
In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely. | instruction | 0 | 58,628 | 19 | 117,256 |
Tags: implementation, probabilities, strings
Correct Solution:
```
s=input()
d=dict()
mod=[]
mx=[]
for k in s:
d[k]=[]
for i in range(len(s)):
d[s[i]].append(i)
index=0
for k in d.keys():
mod.append(d[k])
for k in mod:
mxct=0
ct=0
x=[]
for i in range(len(s)):
ct=0
dic=dict()
for j in k:
elt = s[(j+i)%(len(s))]
if elt in dic:
dic[elt]+=1
else:
dic[elt]=1
for r in dic:
if dic[r]==1:
ct+=1
mxct=max(ct,mxct)
mx.append(mxct)
sm=0
for k in mx:
sm+=k
print(sm/len(s))
``` | output | 1 | 58,628 | 19 | 117,257 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose.
Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability.
Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win.
Input
The only string contains the string s of length l (3 β€ l β€ 5000), consisting of small English letters only.
Output
Print the only number β the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>
Examples
Input
technocup
Output
1.000000000000000
Input
tictictactac
Output
0.333333333333333
Input
bbaabaabbb
Output
0.100000000000000
Note
In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely.
In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely. | instruction | 0 | 58,629 | 19 | 117,258 |
Tags: implementation, probabilities, strings
Correct Solution:
```
str = input()
l = len(str)
a = []
for c in str:
a.append(ord(c) - ord('a'))
a *= 2
tot = [[0] * l for i in range(26)]
for i in range(1, l):
cnt = [[0] * 26 for i in range(26)]
for j in range(l):
cnt[a[j]][a[j + i]] += 1
for j in range(l):
if cnt[a[j]][a[j + i]] == 1:
tot[a[j]][i] += 1
ans = 0
for sub in tot:
ans += max(sub)
print(ans / l)
``` | output | 1 | 58,629 | 19 | 117,259 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose.
Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability.
Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win.
Input
The only string contains the string s of length l (3 β€ l β€ 5000), consisting of small English letters only.
Output
Print the only number β the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>
Examples
Input
technocup
Output
1.000000000000000
Input
tictictactac
Output
0.333333333333333
Input
bbaabaabbb
Output
0.100000000000000
Note
In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely.
In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely. | instruction | 0 | 58,630 | 19 | 117,260 |
Tags: implementation, probabilities, strings
Correct Solution:
```
s = input()
n = len(s)
d = {}
for i in range(n):
if s[i] not in d: d[s[i]] = []
d[s[i]].append(s[i + 1:] + s[:i])
res = 0
for k, l in d.items():
ans = 0
for j in range(n - 1):
seen, s1 = set(), set()
for i in range(len(l)):
if l[i][j] in s1: s1.remove(l[i][j])
elif l[i][j] not in seen:
s1.add(l[i][j])
seen.add(l[i][j])
ans = max(ans, len(s1))
ans /= n
res += ans
print('{:.7f}'.format(res))
``` | output | 1 | 58,630 | 19 | 117,261 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose.
Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability.
Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win.
Input
The only string contains the string s of length l (3 β€ l β€ 5000), consisting of small English letters only.
Output
Print the only number β the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>
Examples
Input
technocup
Output
1.000000000000000
Input
tictictactac
Output
0.333333333333333
Input
bbaabaabbb
Output
0.100000000000000
Note
In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely.
In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely. | instruction | 0 | 58,631 | 19 | 117,262 |
Tags: implementation, probabilities, strings
Correct Solution:
```
s=input()
d=dict()
mod=[]
mx=[]
for k in s:
d[k]=[]
for i in range(len(s)):
d[s[i]].append(i)
index=0
for k in d.keys():
mod.append(d[k])
for k in mod:
mxct=0
ct=0
x=[]
for i in range(len(s)):
ct=0
dic=dict()
for j in k:
elt = s[(j+i)%(len(s))]
if elt in dic.keys():
dic[elt]+=1
else:
dic[elt]=1
for r in dic.keys():
if dic[r]==1:
ct+=1
mxct=max(ct,mxct)
mx.append(mxct)
sm=0
for k in mx:
sm+=k
print(sm/len(s))
``` | output | 1 | 58,631 | 19 | 117,263 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose.
Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability.
Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win.
Input
The only string contains the string s of length l (3 β€ l β€ 5000), consisting of small English letters only.
Output
Print the only number β the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>
Examples
Input
technocup
Output
1.000000000000000
Input
tictictactac
Output
0.333333333333333
Input
bbaabaabbb
Output
0.100000000000000
Note
In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely.
In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely. | instruction | 0 | 58,632 | 19 | 117,264 |
Tags: implementation, probabilities, strings
Correct Solution:
```
import sys
from collections import defaultdict
s = sys.stdin.readline().strip()
n = len(s)
s_mp = defaultdict(list)
for i in range(n):
s_mp[s[i]].append(i)
result = 0
for let, starts in s_mp.items():
max_p = 0.0
for j in range(1, n):
cnter = defaultdict(int)
for start in starts:
cnter[s[(start + j) % n]] += 1
uniq = 0
for i, v in cnter.items():
if v == 1:
uniq += 1
max_p = max(max_p, uniq/len(starts))
total = len(starts)
result += max_p * len(starts)/n
print('{:.8f}'.format(result))
``` | output | 1 | 58,632 | 19 | 117,265 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose.
Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability.
Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win.
Input
The only string contains the string s of length l (3 β€ l β€ 5000), consisting of small English letters only.
Output
Print the only number β the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>
Examples
Input
technocup
Output
1.000000000000000
Input
tictictactac
Output
0.333333333333333
Input
bbaabaabbb
Output
0.100000000000000
Note
In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely.
In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely. | instruction | 0 | 58,633 | 19 | 117,266 |
Tags: implementation, probabilities, strings
Correct Solution:
```
s = str(input())
n = len(s)
t = s+s
P = [[[0]*26 for i in range(26)] for j in range(n)]
for i in range(n):
c1 = ord(t[i])-ord('a')
for j in range(1, n):
c2 = ord(t[i+j])-ord('a')
P[j][c1][c2] += 1
s = set(s)
ans = 0
for c1 in s:
c1 = ord(c1)-ord('a')
M = 0
for j in range(1, n):
temp = 0
for c2 in range(26):
if P[j][c1][c2] == 1:
temp += 1
M = max(M, temp)
ans += M
print(ans/n)
``` | output | 1 | 58,633 | 19 | 117,267 |
Provide a correct Python 3 solution for this coding contest problem.
Problem statement
There is a positive integer sequence $ a_1, a_2, \ ldots, a_N $ of length $ N $.
Consider the following game, which uses this sequence and is played by $ 2 $ players on the play and the play.
* Alternately select one of the following operations for the first move and the second move.
* Select a positive term in the sequence for $ 1 $ and decrement its value by $ 1 $.
* When all terms in the sequence are positive, decrement the values ββof all terms by $ 1 $.
The one who cannot operate first is the loser.
When $ 2 $ players act optimally, ask for the first move or the second move.
Constraint
* $ 1 \ leq N \ leq 2 \ times 10 ^ 5 $
* $ 1 \ leq a_i \ leq 10 ^ 9 $
* All inputs are integers
* * *
input
Input is given from standard input in the following format.
$ N $
$ a_1 $ $ a_2 $ $ ... $ $ a_N $
output
Output `First` when the first move wins, and output` Second` when the second move wins.
* * *
Input example 1
2
1 2
Output example 1
First
The first move has to reduce the value of the $ 1 $ term by $ 1 $ first, and then the second move has to reduce the value of the $ 2 $ term by $ 1 $.
If the first move then decrements the value of the $ 2 $ term by $ 1 $, the value of all terms in the sequence will be $ 0 $, and the second move will not be able to perform any operations.
* * *
Input example 2
Five
3 1 4 1 5
Output example 2
Second
* * *
Input example 3
8
2 4 8 16 32 64 128 256
Output example 3
Second
* * *
Input example 4
3
999999999 1000000000 1000000000
Output example 4
First
Example
Input
2
1 2
Output
First | instruction | 0 | 58,804 | 19 | 117,608 |
"Correct Solution:
```
def solve(N,a):
if N%2 == 1:
return ["Second","First"][sum(a)%2]
else:
if min(a)%2 == 1:
return "First"
return ["Second","First"][sum(a)%2]
if __name__ == "__main__":
N = int(input())
a = list(map(int,input().split()))
print(solve(N,a))
``` | output | 1 | 58,804 | 19 | 117,609 |
Provide a correct Python 3 solution for this coding contest problem.
Problem statement
There is a positive integer sequence $ a_1, a_2, \ ldots, a_N $ of length $ N $.
Consider the following game, which uses this sequence and is played by $ 2 $ players on the play and the play.
* Alternately select one of the following operations for the first move and the second move.
* Select a positive term in the sequence for $ 1 $ and decrement its value by $ 1 $.
* When all terms in the sequence are positive, decrement the values ββof all terms by $ 1 $.
The one who cannot operate first is the loser.
When $ 2 $ players act optimally, ask for the first move or the second move.
Constraint
* $ 1 \ leq N \ leq 2 \ times 10 ^ 5 $
* $ 1 \ leq a_i \ leq 10 ^ 9 $
* All inputs are integers
* * *
input
Input is given from standard input in the following format.
$ N $
$ a_1 $ $ a_2 $ $ ... $ $ a_N $
output
Output `First` when the first move wins, and output` Second` when the second move wins.
* * *
Input example 1
2
1 2
Output example 1
First
The first move has to reduce the value of the $ 1 $ term by $ 1 $ first, and then the second move has to reduce the value of the $ 2 $ term by $ 1 $.
If the first move then decrements the value of the $ 2 $ term by $ 1 $, the value of all terms in the sequence will be $ 0 $, and the second move will not be able to perform any operations.
* * *
Input example 2
Five
3 1 4 1 5
Output example 2
Second
* * *
Input example 3
8
2 4 8 16 32 64 128 256
Output example 3
Second
* * *
Input example 4
3
999999999 1000000000 1000000000
Output example 4
First
Example
Input
2
1 2
Output
First | instruction | 0 | 58,805 | 19 | 117,610 |
"Correct Solution:
```
N=int(input())
A=list(map(int,input().split()))
if N%2==1:
if sum(A)%2==1:
print("First")
else:
print("Second")
else:
if min(A)%2==1:
print("First")
else:
if sum(A)%2==0:
print("Second")
else:
print("First")
``` | output | 1 | 58,805 | 19 | 117,611 |
Provide a correct Python 3 solution for this coding contest problem.
Problem statement
There is a positive integer sequence $ a_1, a_2, \ ldots, a_N $ of length $ N $.
Consider the following game, which uses this sequence and is played by $ 2 $ players on the play and the play.
* Alternately select one of the following operations for the first move and the second move.
* Select a positive term in the sequence for $ 1 $ and decrement its value by $ 1 $.
* When all terms in the sequence are positive, decrement the values ββof all terms by $ 1 $.
The one who cannot operate first is the loser.
When $ 2 $ players act optimally, ask for the first move or the second move.
Constraint
* $ 1 \ leq N \ leq 2 \ times 10 ^ 5 $
* $ 1 \ leq a_i \ leq 10 ^ 9 $
* All inputs are integers
* * *
input
Input is given from standard input in the following format.
$ N $
$ a_1 $ $ a_2 $ $ ... $ $ a_N $
output
Output `First` when the first move wins, and output` Second` when the second move wins.
* * *
Input example 1
2
1 2
Output example 1
First
The first move has to reduce the value of the $ 1 $ term by $ 1 $ first, and then the second move has to reduce the value of the $ 2 $ term by $ 1 $.
If the first move then decrements the value of the $ 2 $ term by $ 1 $, the value of all terms in the sequence will be $ 0 $, and the second move will not be able to perform any operations.
* * *
Input example 2
Five
3 1 4 1 5
Output example 2
Second
* * *
Input example 3
8
2 4 8 16 32 64 128 256
Output example 3
Second
* * *
Input example 4
3
999999999 1000000000 1000000000
Output example 4
First
Example
Input
2
1 2
Output
First | instruction | 0 | 58,806 | 19 | 117,612 |
"Correct Solution:
```
import sys
sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return sys.stdin.readline()[:-1]
def main():
n=II()
aa=LI()
s=sum(aa)
if n%2:
if s%2:ans="First"
else:ans="Second"
else:
mn=min(aa)
if s%2==0 and mn%2==0:ans="Second"
else:ans="First"
print(ans)
main()
``` | output | 1 | 58,806 | 19 | 117,613 |
Provide a correct Python 3 solution for this coding contest problem.
Problem statement
There is a positive integer sequence $ a_1, a_2, \ ldots, a_N $ of length $ N $.
Consider the following game, which uses this sequence and is played by $ 2 $ players on the play and the play.
* Alternately select one of the following operations for the first move and the second move.
* Select a positive term in the sequence for $ 1 $ and decrement its value by $ 1 $.
* When all terms in the sequence are positive, decrement the values ββof all terms by $ 1 $.
The one who cannot operate first is the loser.
When $ 2 $ players act optimally, ask for the first move or the second move.
Constraint
* $ 1 \ leq N \ leq 2 \ times 10 ^ 5 $
* $ 1 \ leq a_i \ leq 10 ^ 9 $
* All inputs are integers
* * *
input
Input is given from standard input in the following format.
$ N $
$ a_1 $ $ a_2 $ $ ... $ $ a_N $
output
Output `First` when the first move wins, and output` Second` when the second move wins.
* * *
Input example 1
2
1 2
Output example 1
First
The first move has to reduce the value of the $ 1 $ term by $ 1 $ first, and then the second move has to reduce the value of the $ 2 $ term by $ 1 $.
If the first move then decrements the value of the $ 2 $ term by $ 1 $, the value of all terms in the sequence will be $ 0 $, and the second move will not be able to perform any operations.
* * *
Input example 2
Five
3 1 4 1 5
Output example 2
Second
* * *
Input example 3
8
2 4 8 16 32 64 128 256
Output example 3
Second
* * *
Input example 4
3
999999999 1000000000 1000000000
Output example 4
First
Example
Input
2
1 2
Output
First | instruction | 0 | 58,807 | 19 | 117,614 |
"Correct Solution:
```
#
# γγ β_βγ
#γγ (ο½₯Οο½₯)
# .οΌ οΌ΅ β½ οΌ΅οΌΌ
# βοΌγεγοΌβ
# βοΌγζ ΌγοΌβ
# βοΌγη₯γοΌβ
# βοΌγι‘γοΌβ
# βοΌγγγοΌβ
# οΏ£
#
import sys
sys.setrecursionlimit(10**6)
input=sys.stdin.readline
from math import floor,sqrt,factorial,hypot,log #log2γͺγο½ο½
from heapq import heappop, heappush, heappushpop
from collections import Counter,defaultdict,deque
from itertools import accumulate,permutations,combinations,product,combinations_with_replacement
from bisect import bisect_left,bisect_right
from copy import deepcopy
from fractions import gcd
from random import randint
def ceil(a,b): return (a+b-1)//b
inf=float('inf')
mod = 10**9+7
def pprint(*A):
for a in A: print(*a,sep='\n')
def INT_(n): return int(n)-1
def MI(): return map(int,input().split())
def MF(): return map(float, input().split())
def MI_(): return map(INT_,input().split())
def LI(): return list(MI())
def LI_(): return [int(x) - 1 for x in input().split()]
def LF(): return list(MF())
def LIN(n:int): return [I() for _ in range(n)]
def LLIN(n: int): return [LI() for _ in range(n)]
def LLIN_(n: int): return [LI_() for _ in range(n)]
def LLI(): return [list(map(int, l.split() )) for l in input()]
def I(): return int(input())
def F(): return float(input())
def ST(): return input().replace('\n', '')
def main():
N=I()
A=LI()
mini=min(A)
if(N&1):
if(sum(A)&1):
print("First")
else:
print("Second")
else:
if(mini&1):
print("First")
else:
if(sum(A)&1):
print("First")
else:
print("Second")
if __name__ == '__main__':
main()
``` | output | 1 | 58,807 | 19 | 117,615 |
Provide a correct Python 3 solution for this coding contest problem.
Problem statement
There is a positive integer sequence $ a_1, a_2, \ ldots, a_N $ of length $ N $.
Consider the following game, which uses this sequence and is played by $ 2 $ players on the play and the play.
* Alternately select one of the following operations for the first move and the second move.
* Select a positive term in the sequence for $ 1 $ and decrement its value by $ 1 $.
* When all terms in the sequence are positive, decrement the values ββof all terms by $ 1 $.
The one who cannot operate first is the loser.
When $ 2 $ players act optimally, ask for the first move or the second move.
Constraint
* $ 1 \ leq N \ leq 2 \ times 10 ^ 5 $
* $ 1 \ leq a_i \ leq 10 ^ 9 $
* All inputs are integers
* * *
input
Input is given from standard input in the following format.
$ N $
$ a_1 $ $ a_2 $ $ ... $ $ a_N $
output
Output `First` when the first move wins, and output` Second` when the second move wins.
* * *
Input example 1
2
1 2
Output example 1
First
The first move has to reduce the value of the $ 1 $ term by $ 1 $ first, and then the second move has to reduce the value of the $ 2 $ term by $ 1 $.
If the first move then decrements the value of the $ 2 $ term by $ 1 $, the value of all terms in the sequence will be $ 0 $, and the second move will not be able to perform any operations.
* * *
Input example 2
Five
3 1 4 1 5
Output example 2
Second
* * *
Input example 3
8
2 4 8 16 32 64 128 256
Output example 3
Second
* * *
Input example 4
3
999999999 1000000000 1000000000
Output example 4
First
Example
Input
2
1 2
Output
First | instruction | 0 | 58,808 | 19 | 117,616 |
"Correct Solution:
```
n = int(input())
a = list(map(int, input().split()))
min_a = min(a)
sum_a = sum(a)
rest = sum_a - n * min_a
def first():
print("First")
exit()
def second():
print("Second")
exit()
if n % 2 == 1:
if sum_a % 2 == 0:second()
if sum_a % 2 == 1:first()
if min_a % 2 == 1:first()
if rest % 2 == 1:first()
if rest % 2 == 0:second()
``` | output | 1 | 58,808 | 19 | 117,617 |
Provide a correct Python 3 solution for this coding contest problem.
Problem statement
There is a positive integer sequence $ a_1, a_2, \ ldots, a_N $ of length $ N $.
Consider the following game, which uses this sequence and is played by $ 2 $ players on the play and the play.
* Alternately select one of the following operations for the first move and the second move.
* Select a positive term in the sequence for $ 1 $ and decrement its value by $ 1 $.
* When all terms in the sequence are positive, decrement the values ββof all terms by $ 1 $.
The one who cannot operate first is the loser.
When $ 2 $ players act optimally, ask for the first move or the second move.
Constraint
* $ 1 \ leq N \ leq 2 \ times 10 ^ 5 $
* $ 1 \ leq a_i \ leq 10 ^ 9 $
* All inputs are integers
* * *
input
Input is given from standard input in the following format.
$ N $
$ a_1 $ $ a_2 $ $ ... $ $ a_N $
output
Output `First` when the first move wins, and output` Second` when the second move wins.
* * *
Input example 1
2
1 2
Output example 1
First
The first move has to reduce the value of the $ 1 $ term by $ 1 $ first, and then the second move has to reduce the value of the $ 2 $ term by $ 1 $.
If the first move then decrements the value of the $ 2 $ term by $ 1 $, the value of all terms in the sequence will be $ 0 $, and the second move will not be able to perform any operations.
* * *
Input example 2
Five
3 1 4 1 5
Output example 2
Second
* * *
Input example 3
8
2 4 8 16 32 64 128 256
Output example 3
Second
* * *
Input example 4
3
999999999 1000000000 1000000000
Output example 4
First
Example
Input
2
1 2
Output
First | instruction | 0 | 58,809 | 19 | 117,618 |
"Correct Solution:
```
n = int(input())
a = list(map(int, input().split()))
sum_a = sum(a)
a = sorted(a)
if n % 2 == 1:
if sum(a) % 2 == 0:
print("Second")
else:
print("First")
else:
if sum_a % 2 == 0 and a[0] % 2 == 0:
print("Second")
else:
print("First")
``` | output | 1 | 58,809 | 19 | 117,619 |
Provide a correct Python 3 solution for this coding contest problem.
Problem statement
There is a positive integer sequence $ a_1, a_2, \ ldots, a_N $ of length $ N $.
Consider the following game, which uses this sequence and is played by $ 2 $ players on the play and the play.
* Alternately select one of the following operations for the first move and the second move.
* Select a positive term in the sequence for $ 1 $ and decrement its value by $ 1 $.
* When all terms in the sequence are positive, decrement the values ββof all terms by $ 1 $.
The one who cannot operate first is the loser.
When $ 2 $ players act optimally, ask for the first move or the second move.
Constraint
* $ 1 \ leq N \ leq 2 \ times 10 ^ 5 $
* $ 1 \ leq a_i \ leq 10 ^ 9 $
* All inputs are integers
* * *
input
Input is given from standard input in the following format.
$ N $
$ a_1 $ $ a_2 $ $ ... $ $ a_N $
output
Output `First` when the first move wins, and output` Second` when the second move wins.
* * *
Input example 1
2
1 2
Output example 1
First
The first move has to reduce the value of the $ 1 $ term by $ 1 $ first, and then the second move has to reduce the value of the $ 2 $ term by $ 1 $.
If the first move then decrements the value of the $ 2 $ term by $ 1 $, the value of all terms in the sequence will be $ 0 $, and the second move will not be able to perform any operations.
* * *
Input example 2
Five
3 1 4 1 5
Output example 2
Second
* * *
Input example 3
8
2 4 8 16 32 64 128 256
Output example 3
Second
* * *
Input example 4
3
999999999 1000000000 1000000000
Output example 4
First
Example
Input
2
1 2
Output
First | instruction | 0 | 58,810 | 19 | 117,620 |
"Correct Solution:
```
N = int(input())
A = list(map(int,input().split()))
if N%2 or 0 in A:
print('First' if sum(A)%2 else 'Second')
exit()
if min(A)%2:
print('First')
else:
print('First' if sum(A)%2 else 'Second')
``` | output | 1 | 58,810 | 19 | 117,621 |
Provide a correct Python 3 solution for this coding contest problem.
Problem statement
There is a positive integer sequence $ a_1, a_2, \ ldots, a_N $ of length $ N $.
Consider the following game, which uses this sequence and is played by $ 2 $ players on the play and the play.
* Alternately select one of the following operations for the first move and the second move.
* Select a positive term in the sequence for $ 1 $ and decrement its value by $ 1 $.
* When all terms in the sequence are positive, decrement the values ββof all terms by $ 1 $.
The one who cannot operate first is the loser.
When $ 2 $ players act optimally, ask for the first move or the second move.
Constraint
* $ 1 \ leq N \ leq 2 \ times 10 ^ 5 $
* $ 1 \ leq a_i \ leq 10 ^ 9 $
* All inputs are integers
* * *
input
Input is given from standard input in the following format.
$ N $
$ a_1 $ $ a_2 $ $ ... $ $ a_N $
output
Output `First` when the first move wins, and output` Second` when the second move wins.
* * *
Input example 1
2
1 2
Output example 1
First
The first move has to reduce the value of the $ 1 $ term by $ 1 $ first, and then the second move has to reduce the value of the $ 2 $ term by $ 1 $.
If the first move then decrements the value of the $ 2 $ term by $ 1 $, the value of all terms in the sequence will be $ 0 $, and the second move will not be able to perform any operations.
* * *
Input example 2
Five
3 1 4 1 5
Output example 2
Second
* * *
Input example 3
8
2 4 8 16 32 64 128 256
Output example 3
Second
* * *
Input example 4
3
999999999 1000000000 1000000000
Output example 4
First
Example
Input
2
1 2
Output
First | instruction | 0 | 58,811 | 19 | 117,622 |
"Correct Solution:
```
#!usr/bin/env python3
from collections import defaultdict, deque
from heapq import heappush, heappop
from itertools import permutations, accumulate
import sys
import math
import bisect
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
res = list(sys.stdin.readline())
if res[-1] == "\n":
return res[:-1]
return res
def IR(n):
return [I() for i in range(n)]
def LIR(n):
return [LI() for i in range(n)]
def SR(n):
return [S() for i in range(n)]
def LSR(n):
return [LS() for i in range(n)]
sys.setrecursionlimit(1000000)
mod = 1000000007
def solve():
n = I()
a = LI()
print(["First","Second"][((n&1)&(1^sum(a)&1))|((1^n&1)&(1^sum(a)&1)&(1^min(a)&1))])
return
#Solve
if __name__ == "__main__":
solve()
``` | output | 1 | 58,811 | 19 | 117,623 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Couple Cover, a wildly popular luck-based game, is about to begin! Two players must work together to construct a rectangle. A bag with n balls, each with an integer written on it, is placed on the table. The first player reaches in and grabs a ball randomly (all balls have equal probability of being chosen) β the number written on this ball is the rectangle's width in meters. This ball is not returned to the bag, and the second player reaches into the bag and grabs another ball β the number written on this ball is the rectangle's height in meters. If the area of the rectangle is greater than or equal some threshold p square meters, the players win. Otherwise, they lose.
The organizers of the game are trying to select an appropriate value for p so that the probability of a couple winning is not too high and not too low, but they are slow at counting, so they have hired you to answer some questions for them. You are given a list of the numbers written on the balls, the organizers would like to know how many winning pairs of balls exist for different values of p. Note that two pairs are different if either the first or the second ball is different between the two in pair, and two different balls with the same number are considered different.
Input
The input begins with a single positive integer n in its own line (1 β€ n β€ 106).
The second line contains n positive integers β the i-th number in this line is equal to ai (1 β€ ai β€ 3Β·106), the number written on the i-th ball.
The next line contains an integer m (1 β€ m β€ 106), the number of questions you are being asked.
Then, the following line contains m positive integers β the j-th number in this line is equal to the value of p (1 β€ p β€ 3Β·106) in the j-th question you are being asked.
Output
For each question, print the number of winning pairs of balls that exist for the given value of p in the separate line.
Examples
Input
5
4 2 6 1 3
4
1 3 5 8
Output
20
18
14
10
Input
2
5 6
2
30 31
Output
2
0
Submitted Solution:
```
N=3*10**6
n = int(input())
l = [int(zax) for zax in input().split()]
q = int(input())
qu = [int(zax) for zax in input().split()]
freq = [0 for i in range(1,N+1)]
under_arr = [0 for i in range(1,N+1)]
answers = [0 for i in range(1,N+1)]
for i in l:
freq[i-1] +=1
for i in range(1,N+1):
for j in range(1,N//i + 1):
if i!=j:
count = freq[i-1]*freq[j-1]
index = i*j
under_arr[index-1]+=count
answers[0]=under_arr[0]
for i in range(2 ,N+1):
answers[i-1]=under_arr[i-1]+answers[i-2]
for q in qu:
if q==1:
num = 0
else:
num = answers[q-2]
print(n*(n-1)-num)
``` | instruction | 0 | 59,315 | 19 | 118,630 |
No | output | 1 | 59,315 | 19 | 118,631 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Couple Cover, a wildly popular luck-based game, is about to begin! Two players must work together to construct a rectangle. A bag with n balls, each with an integer written on it, is placed on the table. The first player reaches in and grabs a ball randomly (all balls have equal probability of being chosen) β the number written on this ball is the rectangle's width in meters. This ball is not returned to the bag, and the second player reaches into the bag and grabs another ball β the number written on this ball is the rectangle's height in meters. If the area of the rectangle is greater than or equal some threshold p square meters, the players win. Otherwise, they lose.
The organizers of the game are trying to select an appropriate value for p so that the probability of a couple winning is not too high and not too low, but they are slow at counting, so they have hired you to answer some questions for them. You are given a list of the numbers written on the balls, the organizers would like to know how many winning pairs of balls exist for different values of p. Note that two pairs are different if either the first or the second ball is different between the two in pair, and two different balls with the same number are considered different.
Input
The input begins with a single positive integer n in its own line (1 β€ n β€ 106).
The second line contains n positive integers β the i-th number in this line is equal to ai (1 β€ ai β€ 3Β·106), the number written on the i-th ball.
The next line contains an integer m (1 β€ m β€ 106), the number of questions you are being asked.
Then, the following line contains m positive integers β the j-th number in this line is equal to the value of p (1 β€ p β€ 3Β·106) in the j-th question you are being asked.
Output
For each question, print the number of winning pairs of balls that exist for the given value of p in the separate line.
Examples
Input
5
4 2 6 1 3
4
1 3 5 8
Output
20
18
14
10
Input
2
5 6
2
30 31
Output
2
0
Submitted Solution:
```
n = int(input())
l = [int(zax) for zax in input().split()]
q = int(input())
qu = [int(zax) for zax in input().split()]
N=min(3*10**6,max(qu))
freq = [0 for i in range(0,N+1)]
under_arr = [0 for i in range(0,N+1)]
answers = [0 for i in range(0,N+1)]
for i in l:
freq[i] +=1
for i in range(1,N+1):
for j in range(1,N//i + 1):
if i!=j:
count = freq[i]*freq[j]
under_arr[i*j]+=count
answers[1]=under_arr[1]
for i in range(2 ,N+1):
answers[i]=under_arr[i]+answers[i-1]
for q in qu:
if q==1:
num = 0
else:
num = answers[q-1]
print(n*(n-1)-num)
``` | instruction | 0 | 59,316 | 19 | 118,632 |
No | output | 1 | 59,316 | 19 | 118,633 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Couple Cover, a wildly popular luck-based game, is about to begin! Two players must work together to construct a rectangle. A bag with n balls, each with an integer written on it, is placed on the table. The first player reaches in and grabs a ball randomly (all balls have equal probability of being chosen) β the number written on this ball is the rectangle's width in meters. This ball is not returned to the bag, and the second player reaches into the bag and grabs another ball β the number written on this ball is the rectangle's height in meters. If the area of the rectangle is greater than or equal some threshold p square meters, the players win. Otherwise, they lose.
The organizers of the game are trying to select an appropriate value for p so that the probability of a couple winning is not too high and not too low, but they are slow at counting, so they have hired you to answer some questions for them. You are given a list of the numbers written on the balls, the organizers would like to know how many winning pairs of balls exist for different values of p. Note that two pairs are different if either the first or the second ball is different between the two in pair, and two different balls with the same number are considered different.
Input
The input begins with a single positive integer n in its own line (1 β€ n β€ 106).
The second line contains n positive integers β the i-th number in this line is equal to ai (1 β€ ai β€ 3Β·106), the number written on the i-th ball.
The next line contains an integer m (1 β€ m β€ 106), the number of questions you are being asked.
Then, the following line contains m positive integers β the j-th number in this line is equal to the value of p (1 β€ p β€ 3Β·106) in the j-th question you are being asked.
Output
For each question, print the number of winning pairs of balls that exist for the given value of p in the separate line.
Examples
Input
5
4 2 6 1 3
4
1 3 5 8
Output
20
18
14
10
Input
2
5 6
2
30 31
Output
2
0
Submitted Solution:
```
def func(list, no):
ct=0
blist = list[:]
for a in list:
for b in blist:
if b is not a:
if a*b >= no:
ct+=1
return ct
n = int(input())
lista = list(map(int, input().split()))
t = int(input())
cover = list(map(int, input().split()))
for i in cover:
print(func(lista, i))
``` | instruction | 0 | 59,317 | 19 | 118,634 |
No | output | 1 | 59,317 | 19 | 118,635 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Couple Cover, a wildly popular luck-based game, is about to begin! Two players must work together to construct a rectangle. A bag with n balls, each with an integer written on it, is placed on the table. The first player reaches in and grabs a ball randomly (all balls have equal probability of being chosen) β the number written on this ball is the rectangle's width in meters. This ball is not returned to the bag, and the second player reaches into the bag and grabs another ball β the number written on this ball is the rectangle's height in meters. If the area of the rectangle is greater than or equal some threshold p square meters, the players win. Otherwise, they lose.
The organizers of the game are trying to select an appropriate value for p so that the probability of a couple winning is not too high and not too low, but they are slow at counting, so they have hired you to answer some questions for them. You are given a list of the numbers written on the balls, the organizers would like to know how many winning pairs of balls exist for different values of p. Note that two pairs are different if either the first or the second ball is different between the two in pair, and two different balls with the same number are considered different.
Input
The input begins with a single positive integer n in its own line (1 β€ n β€ 106).
The second line contains n positive integers β the i-th number in this line is equal to ai (1 β€ ai β€ 3Β·106), the number written on the i-th ball.
The next line contains an integer m (1 β€ m β€ 106), the number of questions you are being asked.
Then, the following line contains m positive integers β the j-th number in this line is equal to the value of p (1 β€ p β€ 3Β·106) in the j-th question you are being asked.
Output
For each question, print the number of winning pairs of balls that exist for the given value of p in the separate line.
Examples
Input
5
4 2 6 1 3
4
1 3 5 8
Output
20
18
14
10
Input
2
5 6
2
30 31
Output
2
0
Submitted Solution:
```
q=int(input())
a = [int(i) for i in input().split()]
w = int(input())
b = [int(i) for i in input().split()]
k=0
for i in b:
for t in a:
for j in range(a.index(t)+1,len(a)):
if t*a[j]>=i:
k+=1
print(k*2)
k=0
#for i in b:
#print(i)
``` | instruction | 0 | 59,318 | 19 | 118,636 |
No | output | 1 | 59,318 | 19 | 118,637 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is never too late to play the fancy "Binary Cards" game!
There is an infinite amount of cards of positive and negative ranks that are used in the game. The absolute value of any card rank is a power of two, i.e. each card has a rank of either 2k or - 2k for some integer k β₯ 0. There is an infinite amount of cards of any valid rank.
At the beginning of the game player forms his deck that is some multiset (possibly empty) of cards. It is allowed to pick any number of cards of any rank but the small deck is considered to be a skill indicator. Game consists of n rounds. In the i-th round jury tells the player an integer ai. After that the player is obligated to draw such a subset of his deck that the sum of ranks of the chosen cards is equal to ai (it is allowed to not draw any cards, in which case the sum is considered to be equal to zero). If player fails to do so, he loses and the game is over. Otherwise, player takes back all of his cards into his deck and the game proceeds to the next round. Player is considered a winner if he is able to draw the suitable set of cards in each of the rounds.
Somebody told you which numbers ai the jury is going to tell you in each round. Now you want to pick a deck consisting of the minimum number of cards that allows you to win the "Binary Cards" game.
Input
The first line of input contains an integer n (1 β€ n β€ 100 000), the number of rounds in the game.
The second line of input contains n integers a1, a2, ..., an ( - 100 000 β€ ai β€ 100 000), the numbers that jury is going to tell in each round.
Output
In the first line print the integer k (0 β€ k β€ 100 000), the minimum number of cards you have to pick in your deck in ordered to win the "Binary Cards".
In the second line print k integers b1, b2, ..., bk ( - 220 β€ bi β€ 220, |bi| is a power of two), the ranks of the cards in your deck. You may output ranks in any order. If there are several optimum decks, you are allowed to print any of them.
It is guaranteed that there exists a deck of minimum size satisfying all the requirements above.
Examples
Input
1
9
Output
2
1 8
Input
5
-1 3 0 4 7
Output
3
4 -1 4
Input
4
2 -2 14 18
Output
3
-2 2 16
Note
In the first sample there is the only round in the game, in which you may simply draw both your cards. Note that this sample test is the only one satisfying the first test group constraints.
In the second sample you may draw the only card - 1 in the first round, cards 4 and - 1 in the second round, nothing in the third round, the only card 4 in the fourth round and the whole deck in the fifth round.
Submitted Solution:
```
input()
sugg = input()
l = set(sugg.split(' '))
def puis(n):
if n == 0:
return 1
return puis(n-1)*2
def binaire(x):
if x in (1,0):
return str(x)
return binaire(x // 2)+str(x % 2)
def check(x, negative=False):
l = []
bin = binaire(x)
for i in range(len(bin)):
if bin[i] != '0':
p = len(bin) -i -1
if not negative:
l.append(puis(p))
else:
l.append(-puis(p))
return set(l)
final=set()
for i in l:
i = int(i)
if int(i)>0:
final.update(check(i))
else:
final.update(check(abs(i),negative=True))
print(len(final))
for i in final:
print(i,end=' ')
``` | instruction | 0 | 59,398 | 19 | 118,796 |
No | output | 1 | 59,398 | 19 | 118,797 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Utkarsh is forced to play yet another one of Ashish's games. The game progresses turn by turn and as usual, Ashish moves first.
Consider the 2D plane. There is a token which is initially at (0,0). In one move a player must increase either the x coordinate or the y coordinate of the token by exactly k. In doing so, the player must ensure that the token stays within a (Euclidean) distance d from (0,0).
In other words, if after a move the coordinates of the token are (p,q), then p^2 + q^2 β€ d^2 must hold.
The game ends when a player is unable to make a move. It can be shown that the game will end in a finite number of moves. If both players play optimally, determine who will win.
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of test cases.
The only line of each test case contains two space separated integers d (1 β€ d β€ 10^5) and k (1 β€ k β€ d).
Output
For each test case, if Ashish wins the game, print "Ashish", otherwise print "Utkarsh" (without the quotes).
Example
Input
5
2 1
5 2
10 3
25 4
15441 33
Output
Utkarsh
Ashish
Utkarsh
Utkarsh
Ashish
Note
In the first test case, one possible sequence of moves can be
(0, 0) \xrightarrow{Ashish } (0, 1) \xrightarrow{Utkarsh } (0, 2).
Ashish has no moves left, so Utkarsh wins.
<image>
Submitted Solution:
```
t = int(input())
for ti in range(t):
n, k = map(int, input().split())
x = int((n / k)/2**0.5)
if (x+1)**2 + (x)**2 <= (n/k)**2:
print('Ashish')
else:
print('Utkarsh')
``` | instruction | 0 | 59,940 | 19 | 119,880 |
Yes | output | 1 | 59,940 | 19 | 119,881 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Utkarsh is forced to play yet another one of Ashish's games. The game progresses turn by turn and as usual, Ashish moves first.
Consider the 2D plane. There is a token which is initially at (0,0). In one move a player must increase either the x coordinate or the y coordinate of the token by exactly k. In doing so, the player must ensure that the token stays within a (Euclidean) distance d from (0,0).
In other words, if after a move the coordinates of the token are (p,q), then p^2 + q^2 β€ d^2 must hold.
The game ends when a player is unable to make a move. It can be shown that the game will end in a finite number of moves. If both players play optimally, determine who will win.
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of test cases.
The only line of each test case contains two space separated integers d (1 β€ d β€ 10^5) and k (1 β€ k β€ d).
Output
For each test case, if Ashish wins the game, print "Ashish", otherwise print "Utkarsh" (without the quotes).
Example
Input
5
2 1
5 2
10 3
25 4
15441 33
Output
Utkarsh
Ashish
Utkarsh
Utkarsh
Ashish
Note
In the first test case, one possible sequence of moves can be
(0, 0) \xrightarrow{Ashish } (0, 1) \xrightarrow{Utkarsh } (0, 2).
Ashish has no moves left, so Utkarsh wins.
<image>
Submitted Solution:
```
import os
import sys
from io import BytesIO, IOBase
import math
def main():
pass
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
def binary(n):
return (bin(n).replace("0b", ""))
def decimal(s):
return (int(s, 2))
def pow2(n):
p = 0
while (n > 1):
n //= 2
p += 1
return (p)
def primeFactors(n):
l=[]
while n % 2 == 0:
l.append(2)
n = n / 2
for i in range(3, int(math.sqrt(n)) + 1, 2):
while n % i == 0:
l.append(i)
n = n / i
if n > 2:
l.append(int(n))
return (l)
def isPrime(n):
if (n == 1):
return (False)
else:
root = int(n ** 0.5)
root += 1
for i in range(2, root):
if (n % i == 0):
return (False)
return (True)
def maxPrimeFactors(n):
maxPrime = -1
while n % 2 == 0:
maxPrime = 2
n >>= 1
for i in range(3, int(math.sqrt(n)) + 1, 2):
while n % i == 0:
maxPrime = i
n = n / i
if n > 2:
maxPrime = n
return int(maxPrime)
def countcon(s,i):
c=0
ch=s[i]
for i in range(i,len(s)):
if(s[i]==ch):
c+=1
else:
break
return(c)
def lis(arr):
n = len(arr)
lis = [1] * n
for i in range(1, n):
for j in range(0, i):
if arr[i] > arr[j] and lis[i] < lis[j] + 1:
lis[i] = lis[j] + 1
maximum = 0
for i in range(n):
maximum = max(maximum, lis[i])
return maximum
def isSubSequence(str1, str2):
m = len(str1)
n = len(str2)
j = 0
i = 0
while j < m and i < n:
if str1[j] == str2[i]:
j = j + 1
i = i + 1
return j == m
def maxfac(n):
root=int(n**0.5)
for i in range(2,root+1):
if(n%i==0):
return(n//i)
return(n)
for xyz in range(0,int(input())):
d,k=map(int,input().split())
m=int(((d*d)/(2*k*k))**0.5)
tt=2*m
tx=ty=m*k
tx+=k
if(tx*tx+ty*ty<=d*d):
tt+=1
#print(m,tt)
if(tt%2==0):
print("Utkarsh")
else:
print("Ashish")
``` | instruction | 0 | 59,941 | 19 | 119,882 |
Yes | output | 1 | 59,941 | 19 | 119,883 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Utkarsh is forced to play yet another one of Ashish's games. The game progresses turn by turn and as usual, Ashish moves first.
Consider the 2D plane. There is a token which is initially at (0,0). In one move a player must increase either the x coordinate or the y coordinate of the token by exactly k. In doing so, the player must ensure that the token stays within a (Euclidean) distance d from (0,0).
In other words, if after a move the coordinates of the token are (p,q), then p^2 + q^2 β€ d^2 must hold.
The game ends when a player is unable to make a move. It can be shown that the game will end in a finite number of moves. If both players play optimally, determine who will win.
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of test cases.
The only line of each test case contains two space separated integers d (1 β€ d β€ 10^5) and k (1 β€ k β€ d).
Output
For each test case, if Ashish wins the game, print "Ashish", otherwise print "Utkarsh" (without the quotes).
Example
Input
5
2 1
5 2
10 3
25 4
15441 33
Output
Utkarsh
Ashish
Utkarsh
Utkarsh
Ashish
Note
In the first test case, one possible sequence of moves can be
(0, 0) \xrightarrow{Ashish } (0, 1) \xrightarrow{Utkarsh } (0, 2).
Ashish has no moves left, so Utkarsh wins.
<image>
Submitted Solution:
```
for x in range(int(input())):
d,k=map(int,input().split())
a=((d*d)//2)**0.5
a=a-(a%k)
b=a+k
if (a*a+b*b)<=d*d:
print("Ashish")
else:
print("Utkarsh")
``` | instruction | 0 | 59,942 | 19 | 119,884 |
Yes | output | 1 | 59,942 | 19 | 119,885 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Utkarsh is forced to play yet another one of Ashish's games. The game progresses turn by turn and as usual, Ashish moves first.
Consider the 2D plane. There is a token which is initially at (0,0). In one move a player must increase either the x coordinate or the y coordinate of the token by exactly k. In doing so, the player must ensure that the token stays within a (Euclidean) distance d from (0,0).
In other words, if after a move the coordinates of the token are (p,q), then p^2 + q^2 β€ d^2 must hold.
The game ends when a player is unable to make a move. It can be shown that the game will end in a finite number of moves. If both players play optimally, determine who will win.
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of test cases.
The only line of each test case contains two space separated integers d (1 β€ d β€ 10^5) and k (1 β€ k β€ d).
Output
For each test case, if Ashish wins the game, print "Ashish", otherwise print "Utkarsh" (without the quotes).
Example
Input
5
2 1
5 2
10 3
25 4
15441 33
Output
Utkarsh
Ashish
Utkarsh
Utkarsh
Ashish
Note
In the first test case, one possible sequence of moves can be
(0, 0) \xrightarrow{Ashish } (0, 1) \xrightarrow{Utkarsh } (0, 2).
Ashish has no moves left, so Utkarsh wins.
<image>
Submitted Solution:
```
t=int(input())
new=[]
for i in range(t):
a=list(map(int,input().split()))
new.append(a)
for i in new:
b=i[0]//i[1]
c=i[0]%i[1]
if (b+c)%2==0:
print('Utkarsh')
else:
print('Ashish')
``` | instruction | 0 | 59,944 | 19 | 119,888 |
No | output | 1 | 59,944 | 19 | 119,889 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Utkarsh is forced to play yet another one of Ashish's games. The game progresses turn by turn and as usual, Ashish moves first.
Consider the 2D plane. There is a token which is initially at (0,0). In one move a player must increase either the x coordinate or the y coordinate of the token by exactly k. In doing so, the player must ensure that the token stays within a (Euclidean) distance d from (0,0).
In other words, if after a move the coordinates of the token are (p,q), then p^2 + q^2 β€ d^2 must hold.
The game ends when a player is unable to make a move. It can be shown that the game will end in a finite number of moves. If both players play optimally, determine who will win.
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of test cases.
The only line of each test case contains two space separated integers d (1 β€ d β€ 10^5) and k (1 β€ k β€ d).
Output
For each test case, if Ashish wins the game, print "Ashish", otherwise print "Utkarsh" (without the quotes).
Example
Input
5
2 1
5 2
10 3
25 4
15441 33
Output
Utkarsh
Ashish
Utkarsh
Utkarsh
Ashish
Note
In the first test case, one possible sequence of moves can be
(0, 0) \xrightarrow{Ashish } (0, 1) \xrightarrow{Utkarsh } (0, 2).
Ashish has no moves left, so Utkarsh wins.
<image>
Submitted Solution:
```
def inp():
return(int(input()))
def inlt():
return(list(map(int,input().split())))
def insr():
s = input()
return(list(s[:len(s) ]))
def invr():
return(map(int,input().split()))
y = inp()
for _ in range(y):
[d,k] = inlt()
x = 0
while(2*(x**2) <= d**2):
x+= 1
x -= 1
#print(x)
if(k%2 == 0):
if((2*x)%(k*2) < k):
print("Utkarsh")
else:
print("Ashish")
else:
#(x,x+2)
if((x+1)**2 + (x-1)**2 > d**2):
dist = (x+1)**2 + (x-1)**2 - d**2
total_step = 2*x - dist
if(total_step%(k*2) < k):
print("Utkarsh")
else:
print("Ashish")
else:
if((2*x)%(k*2) < k):
print("Utkarsh")
else:
print("Ashish")
#goal is to reach x,y such that x+y +k > d^2
``` | instruction | 0 | 59,945 | 19 | 119,890 |
No | output | 1 | 59,945 | 19 | 119,891 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Utkarsh is forced to play yet another one of Ashish's games. The game progresses turn by turn and as usual, Ashish moves first.
Consider the 2D plane. There is a token which is initially at (0,0). In one move a player must increase either the x coordinate or the y coordinate of the token by exactly k. In doing so, the player must ensure that the token stays within a (Euclidean) distance d from (0,0).
In other words, if after a move the coordinates of the token are (p,q), then p^2 + q^2 β€ d^2 must hold.
The game ends when a player is unable to make a move. It can be shown that the game will end in a finite number of moves. If both players play optimally, determine who will win.
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of test cases.
The only line of each test case contains two space separated integers d (1 β€ d β€ 10^5) and k (1 β€ k β€ d).
Output
For each test case, if Ashish wins the game, print "Ashish", otherwise print "Utkarsh" (without the quotes).
Example
Input
5
2 1
5 2
10 3
25 4
15441 33
Output
Utkarsh
Ashish
Utkarsh
Utkarsh
Ashish
Note
In the first test case, one possible sequence of moves can be
(0, 0) \xrightarrow{Ashish } (0, 1) \xrightarrow{Utkarsh } (0, 2).
Ashish has no moves left, so Utkarsh wins.
<image>
Submitted Solution:
```
#import os
#import sys
#from io import BytesIO, IOBase
#import itertools
import math
#import operator as op
#from functools import cmp_to_key
#import threading
#from heapq import heappop, heappush, heapify
#import random
#import bisect
#from queue import PriorityQueue, Queue
#from collections import defaultdict, deque
#import itertools
#import math
#import operator as op
#import random
#from functools import cmp_to_key
def ic(n,a,s=0,st=1): return [a for i in range(s,n,st)]
def ri(): return int(input())
def sa(): return map(int,input().split())
def ra(): return list(map(int,input().split()))
def mati(n): return [ra() for i in range(n)]
for _ in range(int(input())):
d,k =sa()
d1=int(math.sqrt(2*d*d/(k*k)))
print(['Utkarsh','Ashish'][d1&1])
``` | instruction | 0 | 59,946 | 19 | 119,892 |
No | output | 1 | 59,946 | 19 | 119,893 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Utkarsh is forced to play yet another one of Ashish's games. The game progresses turn by turn and as usual, Ashish moves first.
Consider the 2D plane. There is a token which is initially at (0,0). In one move a player must increase either the x coordinate or the y coordinate of the token by exactly k. In doing so, the player must ensure that the token stays within a (Euclidean) distance d from (0,0).
In other words, if after a move the coordinates of the token are (p,q), then p^2 + q^2 β€ d^2 must hold.
The game ends when a player is unable to make a move. It can be shown that the game will end in a finite number of moves. If both players play optimally, determine who will win.
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of test cases.
The only line of each test case contains two space separated integers d (1 β€ d β€ 10^5) and k (1 β€ k β€ d).
Output
For each test case, if Ashish wins the game, print "Ashish", otherwise print "Utkarsh" (without the quotes).
Example
Input
5
2 1
5 2
10 3
25 4
15441 33
Output
Utkarsh
Ashish
Utkarsh
Utkarsh
Ashish
Note
In the first test case, one possible sequence of moves can be
(0, 0) \xrightarrow{Ashish } (0, 1) \xrightarrow{Utkarsh } (0, 2).
Ashish has no moves left, so Utkarsh wins.
<image>
Submitted Solution:
```
import sys
input = sys.stdin.readline
for _ in range(int(input())):
d,k=[int(x) for x in input().split()]
x,y=0,0
while (x**2)+(y**2)<d**2:
if x<=y:
x+=k
else:
y+=k
if x==y:
print('Ashish')
else:
print('Utkarsh')
``` | instruction | 0 | 59,947 | 19 | 119,894 |
No | output | 1 | 59,947 | 19 | 119,895 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Sherlock Holmes and Dr. Watson played some game on a checkered board n Γ n in size. During the game they put numbers on the board's squares by some tricky rules we don't know. However, the game is now over and each square of the board contains exactly one number. To understand who has won, they need to count the number of winning squares. To determine if the particular square is winning you should do the following. Calculate the sum of all numbers on the squares that share this column (including the given square) and separately calculate the sum of all numbers on the squares that share this row (including the given square). A square is considered winning if the sum of the column numbers is strictly greater than the sum of the row numbers.
<image>
For instance, lets game was ended like is shown in the picture. Then the purple cell is winning, because the sum of its column numbers equals 8 + 3 + 6 + 7 = 24, sum of its row numbers equals 9 + 5 + 3 + 2 = 19, and 24 > 19.
Input
The first line contains an integer n (1 β€ n β€ 30). Each of the following n lines contain n space-separated integers. The j-th number on the i-th line represents the number on the square that belongs to the j-th column and the i-th row on the board. All number on the board are integers from 1 to 100.
Output
Print the single number β the number of the winning squares.
Examples
Input
1
1
Output
0
Input
2
1 2
3 4
Output
2
Input
4
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Output
6
Note
In the first example two upper squares are winning.
In the third example three left squares in the both middle rows are winning:
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
| instruction | 0 | 59,991 | 19 | 119,982 |
Tags: brute force
Correct Solution:
```
n = int(input())
a = []
h = []
v = []
for i in range(n):
a.append([int(x) for x in input().split()])
for l in a:
h.append(sum(l))
for l in zip(*a):
v.append(sum(l))
ans = 0
for x in h:
for y in v:
if y > x:
ans += 1
print(ans)
``` | output | 1 | 59,991 | 19 | 119,983 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Sherlock Holmes and Dr. Watson played some game on a checkered board n Γ n in size. During the game they put numbers on the board's squares by some tricky rules we don't know. However, the game is now over and each square of the board contains exactly one number. To understand who has won, they need to count the number of winning squares. To determine if the particular square is winning you should do the following. Calculate the sum of all numbers on the squares that share this column (including the given square) and separately calculate the sum of all numbers on the squares that share this row (including the given square). A square is considered winning if the sum of the column numbers is strictly greater than the sum of the row numbers.
<image>
For instance, lets game was ended like is shown in the picture. Then the purple cell is winning, because the sum of its column numbers equals 8 + 3 + 6 + 7 = 24, sum of its row numbers equals 9 + 5 + 3 + 2 = 19, and 24 > 19.
Input
The first line contains an integer n (1 β€ n β€ 30). Each of the following n lines contain n space-separated integers. The j-th number on the i-th line represents the number on the square that belongs to the j-th column and the i-th row on the board. All number on the board are integers from 1 to 100.
Output
Print the single number β the number of the winning squares.
Examples
Input
1
1
Output
0
Input
2
1 2
3 4
Output
2
Input
4
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Output
6
Note
In the first example two upper squares are winning.
In the third example three left squares in the both middle rows are winning:
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
| instruction | 0 | 59,992 | 19 | 119,984 |
Tags: brute force
Correct Solution:
```
def input_matrix(n):
matrix = []
for i in range(n):
matrix.append(list(map(int, input().split())))
return matrix
def get_sum_in_row(a, i):
return sum(a[i])
def get_sum_in_col(a, j):
return sum((a[i][j] for i in range(len(a))))
n = int(input())
a = input_matrix(n)
row_sums = [get_sum_in_row(a, i) for i in range(n)]
col_sums = [get_sum_in_col(a, j) for j in range(n)]
n_ceils = 0
for row_sum in row_sums:
for col_sum in col_sums:
if col_sum > row_sum:
n_ceils += 1
print(n_ceils)
``` | output | 1 | 59,992 | 19 | 119,985 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Sherlock Holmes and Dr. Watson played some game on a checkered board n Γ n in size. During the game they put numbers on the board's squares by some tricky rules we don't know. However, the game is now over and each square of the board contains exactly one number. To understand who has won, they need to count the number of winning squares. To determine if the particular square is winning you should do the following. Calculate the sum of all numbers on the squares that share this column (including the given square) and separately calculate the sum of all numbers on the squares that share this row (including the given square). A square is considered winning if the sum of the column numbers is strictly greater than the sum of the row numbers.
<image>
For instance, lets game was ended like is shown in the picture. Then the purple cell is winning, because the sum of its column numbers equals 8 + 3 + 6 + 7 = 24, sum of its row numbers equals 9 + 5 + 3 + 2 = 19, and 24 > 19.
Input
The first line contains an integer n (1 β€ n β€ 30). Each of the following n lines contain n space-separated integers. The j-th number on the i-th line represents the number on the square that belongs to the j-th column and the i-th row on the board. All number on the board are integers from 1 to 100.
Output
Print the single number β the number of the winning squares.
Examples
Input
1
1
Output
0
Input
2
1 2
3 4
Output
2
Input
4
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Output
6
Note
In the first example two upper squares are winning.
In the third example three left squares in the both middle rows are winning:
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
| instruction | 0 | 59,993 | 19 | 119,986 |
Tags: brute force
Correct Solution:
```
import sys
def input(): return sys.stdin.readline().strip()
def iinput(): return int(input())
def rinput(): return map(int, sys.stdin.readline().strip().split())
def get_list(): return list(map(int, sys.stdin.readline().strip().split()))
n=iinput()
s=[]
for i in range(n):
s.append(list(map(int,input().split())))
coloumn=[]
row=[]
for i in range(n):
count=0
for j in range(n):
count+=s[j][i]
coloumn.append(count)
for i in range(n):
row.append(sum(s[i]))
win=0
for i in range(len(coloumn)):
for j in range(len(row)):
if(coloumn[i]>row[j]):
win+=1
print(win)
``` | output | 1 | 59,993 | 19 | 119,987 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Sherlock Holmes and Dr. Watson played some game on a checkered board n Γ n in size. During the game they put numbers on the board's squares by some tricky rules we don't know. However, the game is now over and each square of the board contains exactly one number. To understand who has won, they need to count the number of winning squares. To determine if the particular square is winning you should do the following. Calculate the sum of all numbers on the squares that share this column (including the given square) and separately calculate the sum of all numbers on the squares that share this row (including the given square). A square is considered winning if the sum of the column numbers is strictly greater than the sum of the row numbers.
<image>
For instance, lets game was ended like is shown in the picture. Then the purple cell is winning, because the sum of its column numbers equals 8 + 3 + 6 + 7 = 24, sum of its row numbers equals 9 + 5 + 3 + 2 = 19, and 24 > 19.
Input
The first line contains an integer n (1 β€ n β€ 30). Each of the following n lines contain n space-separated integers. The j-th number on the i-th line represents the number on the square that belongs to the j-th column and the i-th row on the board. All number on the board are integers from 1 to 100.
Output
Print the single number β the number of the winning squares.
Examples
Input
1
1
Output
0
Input
2
1 2
3 4
Output
2
Input
4
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Output
6
Note
In the first example two upper squares are winning.
In the third example three left squares in the both middle rows are winning:
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
| instruction | 0 | 59,994 | 19 | 119,988 |
Tags: brute force
Correct Solution:
```
n, A = int(input()), []
for i in range(n): A.append([int(x) for x in input().split()])
print(sum(1 for i in range(n) for j in range(n) if sum(A[i]) < sum(list(zip(*A))[j])))
``` | output | 1 | 59,994 | 19 | 119,989 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Sherlock Holmes and Dr. Watson played some game on a checkered board n Γ n in size. During the game they put numbers on the board's squares by some tricky rules we don't know. However, the game is now over and each square of the board contains exactly one number. To understand who has won, they need to count the number of winning squares. To determine if the particular square is winning you should do the following. Calculate the sum of all numbers on the squares that share this column (including the given square) and separately calculate the sum of all numbers on the squares that share this row (including the given square). A square is considered winning if the sum of the column numbers is strictly greater than the sum of the row numbers.
<image>
For instance, lets game was ended like is shown in the picture. Then the purple cell is winning, because the sum of its column numbers equals 8 + 3 + 6 + 7 = 24, sum of its row numbers equals 9 + 5 + 3 + 2 = 19, and 24 > 19.
Input
The first line contains an integer n (1 β€ n β€ 30). Each of the following n lines contain n space-separated integers. The j-th number on the i-th line represents the number on the square that belongs to the j-th column and the i-th row on the board. All number on the board are integers from 1 to 100.
Output
Print the single number β the number of the winning squares.
Examples
Input
1
1
Output
0
Input
2
1 2
3 4
Output
2
Input
4
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Output
6
Note
In the first example two upper squares are winning.
In the third example three left squares in the both middle rows are winning:
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
| instruction | 0 | 59,995 | 19 | 119,990 |
Tags: brute force
Correct Solution:
```
n = int(input())
l = []
ans = 0
for _ in range(n):
a = [int(y) for y in input().split()]
l.append(a)
def col(w):
h = 0
for u in range(n):
h += l[u][w]
return h
def row(p, q):
g = sum(l[p])
if col(q) > g:
return True
else:
return False
for i in range(n):
for j in range(n):
if row(i, j):
ans += 1
print(ans)
``` | output | 1 | 59,995 | 19 | 119,991 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Sherlock Holmes and Dr. Watson played some game on a checkered board n Γ n in size. During the game they put numbers on the board's squares by some tricky rules we don't know. However, the game is now over and each square of the board contains exactly one number. To understand who has won, they need to count the number of winning squares. To determine if the particular square is winning you should do the following. Calculate the sum of all numbers on the squares that share this column (including the given square) and separately calculate the sum of all numbers on the squares that share this row (including the given square). A square is considered winning if the sum of the column numbers is strictly greater than the sum of the row numbers.
<image>
For instance, lets game was ended like is shown in the picture. Then the purple cell is winning, because the sum of its column numbers equals 8 + 3 + 6 + 7 = 24, sum of its row numbers equals 9 + 5 + 3 + 2 = 19, and 24 > 19.
Input
The first line contains an integer n (1 β€ n β€ 30). Each of the following n lines contain n space-separated integers. The j-th number on the i-th line represents the number on the square that belongs to the j-th column and the i-th row on the board. All number on the board are integers from 1 to 100.
Output
Print the single number β the number of the winning squares.
Examples
Input
1
1
Output
0
Input
2
1 2
3 4
Output
2
Input
4
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Output
6
Note
In the first example two upper squares are winning.
In the third example three left squares in the both middle rows are winning:
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
| instruction | 0 | 59,996 | 19 | 119,992 |
Tags: brute force
Correct Solution:
```
n=int(input())
R=[]
C=[0]*n
L=[]
for i in range(n):
x=list(map(int,input().split()))
s=0
for i in range(n):
s+=x[i]
C[i]+=x[i]
R.append(s)
ans=0
for i in range(n):
for j in range(n):
if(C[j]>R[i]):
ans+=1
print(ans)
``` | output | 1 | 59,996 | 19 | 119,993 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Sherlock Holmes and Dr. Watson played some game on a checkered board n Γ n in size. During the game they put numbers on the board's squares by some tricky rules we don't know. However, the game is now over and each square of the board contains exactly one number. To understand who has won, they need to count the number of winning squares. To determine if the particular square is winning you should do the following. Calculate the sum of all numbers on the squares that share this column (including the given square) and separately calculate the sum of all numbers on the squares that share this row (including the given square). A square is considered winning if the sum of the column numbers is strictly greater than the sum of the row numbers.
<image>
For instance, lets game was ended like is shown in the picture. Then the purple cell is winning, because the sum of its column numbers equals 8 + 3 + 6 + 7 = 24, sum of its row numbers equals 9 + 5 + 3 + 2 = 19, and 24 > 19.
Input
The first line contains an integer n (1 β€ n β€ 30). Each of the following n lines contain n space-separated integers. The j-th number on the i-th line represents the number on the square that belongs to the j-th column and the i-th row on the board. All number on the board are integers from 1 to 100.
Output
Print the single number β the number of the winning squares.
Examples
Input
1
1
Output
0
Input
2
1 2
3 4
Output
2
Input
4
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Output
6
Note
In the first example two upper squares are winning.
In the third example three left squares in the both middle rows are winning:
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
| instruction | 0 | 59,997 | 19 | 119,994 |
Tags: brute force
Correct Solution:
```
n = int(input())
a = [list(map(int, input().split()))for _ in range(n)]
result=0
b = [sum(x) for x in zip(*a)]
c = list()
for i in range(n):
c.append(sum(a[i]))
for i in range(n):
for j in range(n):
if b[i]>c[j]:
result+=1
print(result)
``` | output | 1 | 59,997 | 19 | 119,995 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Sherlock Holmes and Dr. Watson played some game on a checkered board n Γ n in size. During the game they put numbers on the board's squares by some tricky rules we don't know. However, the game is now over and each square of the board contains exactly one number. To understand who has won, they need to count the number of winning squares. To determine if the particular square is winning you should do the following. Calculate the sum of all numbers on the squares that share this column (including the given square) and separately calculate the sum of all numbers on the squares that share this row (including the given square). A square is considered winning if the sum of the column numbers is strictly greater than the sum of the row numbers.
<image>
For instance, lets game was ended like is shown in the picture. Then the purple cell is winning, because the sum of its column numbers equals 8 + 3 + 6 + 7 = 24, sum of its row numbers equals 9 + 5 + 3 + 2 = 19, and 24 > 19.
Input
The first line contains an integer n (1 β€ n β€ 30). Each of the following n lines contain n space-separated integers. The j-th number on the i-th line represents the number on the square that belongs to the j-th column and the i-th row on the board. All number on the board are integers from 1 to 100.
Output
Print the single number β the number of the winning squares.
Examples
Input
1
1
Output
0
Input
2
1 2
3 4
Output
2
Input
4
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Output
6
Note
In the first example two upper squares are winning.
In the third example three left squares in the both middle rows are winning:
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
| instruction | 0 | 59,998 | 19 | 119,996 |
Tags: brute force
Correct Solution:
```
n=int(input())
a=[[*map(int,input().split())]for _ in[0]*n]
b=[*zip(*a)]
r=0
for i in range(n):
for j in range(n):
if sum(b[j])>sum(a[i]):
r+=1
print(r)
``` | output | 1 | 59,998 | 19 | 119,997 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Sherlock Holmes and Dr. Watson played some game on a checkered board n Γ n in size. During the game they put numbers on the board's squares by some tricky rules we don't know. However, the game is now over and each square of the board contains exactly one number. To understand who has won, they need to count the number of winning squares. To determine if the particular square is winning you should do the following. Calculate the sum of all numbers on the squares that share this column (including the given square) and separately calculate the sum of all numbers on the squares that share this row (including the given square). A square is considered winning if the sum of the column numbers is strictly greater than the sum of the row numbers.
<image>
For instance, lets game was ended like is shown in the picture. Then the purple cell is winning, because the sum of its column numbers equals 8 + 3 + 6 + 7 = 24, sum of its row numbers equals 9 + 5 + 3 + 2 = 19, and 24 > 19.
Input
The first line contains an integer n (1 β€ n β€ 30). Each of the following n lines contain n space-separated integers. The j-th number on the i-th line represents the number on the square that belongs to the j-th column and the i-th row on the board. All number on the board are integers from 1 to 100.
Output
Print the single number β the number of the winning squares.
Examples
Input
1
1
Output
0
Input
2
1 2
3 4
Output
2
Input
4
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Output
6
Note
In the first example two upper squares are winning.
In the third example three left squares in the both middle rows are winning:
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Submitted Solution:
```
n = int(input())
arr = []
for i in range(n):
arr.append(list(map(int, input().split())))
row_sum = []
col_sum = []
for i in range(n):
row_sum.append(sum(arr[i]))
for i in range(n):
temp = 0
for j in range(n):
temp += arr[j][i]
col_sum.append(temp)
ans = 0
for i in range(n):
for j in range(n):
if col_sum[i] > row_sum[j]:
ans +=1
print(ans)
``` | instruction | 0 | 59,999 | 19 | 119,998 |
Yes | output | 1 | 59,999 | 19 | 119,999 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Sherlock Holmes and Dr. Watson played some game on a checkered board n Γ n in size. During the game they put numbers on the board's squares by some tricky rules we don't know. However, the game is now over and each square of the board contains exactly one number. To understand who has won, they need to count the number of winning squares. To determine if the particular square is winning you should do the following. Calculate the sum of all numbers on the squares that share this column (including the given square) and separately calculate the sum of all numbers on the squares that share this row (including the given square). A square is considered winning if the sum of the column numbers is strictly greater than the sum of the row numbers.
<image>
For instance, lets game was ended like is shown in the picture. Then the purple cell is winning, because the sum of its column numbers equals 8 + 3 + 6 + 7 = 24, sum of its row numbers equals 9 + 5 + 3 + 2 = 19, and 24 > 19.
Input
The first line contains an integer n (1 β€ n β€ 30). Each of the following n lines contain n space-separated integers. The j-th number on the i-th line represents the number on the square that belongs to the j-th column and the i-th row on the board. All number on the board are integers from 1 to 100.
Output
Print the single number β the number of the winning squares.
Examples
Input
1
1
Output
0
Input
2
1 2
3 4
Output
2
Input
4
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Output
6
Note
In the first example two upper squares are winning.
In the third example three left squares in the both middle rows are winning:
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Submitted Solution:
```
# coding: utf-8
n = int(input())
m = [[int(j) for j in input().split()] for i in range(n)]
rowsum = [sum(i) for i in m]
colsum = [sum([row[i] for row in m]) for i in range(n)]
ans = 0
for i in range(n):
for j in range(n):
if rowsum[i]<colsum[j]:
ans += 1
print(ans)
``` | instruction | 0 | 60,000 | 19 | 120,000 |
Yes | output | 1 | 60,000 | 19 | 120,001 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Sherlock Holmes and Dr. Watson played some game on a checkered board n Γ n in size. During the game they put numbers on the board's squares by some tricky rules we don't know. However, the game is now over and each square of the board contains exactly one number. To understand who has won, they need to count the number of winning squares. To determine if the particular square is winning you should do the following. Calculate the sum of all numbers on the squares that share this column (including the given square) and separately calculate the sum of all numbers on the squares that share this row (including the given square). A square is considered winning if the sum of the column numbers is strictly greater than the sum of the row numbers.
<image>
For instance, lets game was ended like is shown in the picture. Then the purple cell is winning, because the sum of its column numbers equals 8 + 3 + 6 + 7 = 24, sum of its row numbers equals 9 + 5 + 3 + 2 = 19, and 24 > 19.
Input
The first line contains an integer n (1 β€ n β€ 30). Each of the following n lines contain n space-separated integers. The j-th number on the i-th line represents the number on the square that belongs to the j-th column and the i-th row on the board. All number on the board are integers from 1 to 100.
Output
Print the single number β the number of the winning squares.
Examples
Input
1
1
Output
0
Input
2
1 2
3 4
Output
2
Input
4
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Output
6
Note
In the first example two upper squares are winning.
In the third example three left squares in the both middle rows are winning:
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Submitted Solution:
```
n=int(input());l=[];r,c=[],[0]*n;a=0
for i in range(n):
t=list(map(int,input().split()))
l.append(t);r.append(sum(t))
for j in range(n):c[j]+=t[j]
for i in range(n):
for j in range(n):
if r[i]<c[j]:a+=1
print(a)
``` | instruction | 0 | 60,001 | 19 | 120,002 |
Yes | output | 1 | 60,001 | 19 | 120,003 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Sherlock Holmes and Dr. Watson played some game on a checkered board n Γ n in size. During the game they put numbers on the board's squares by some tricky rules we don't know. However, the game is now over and each square of the board contains exactly one number. To understand who has won, they need to count the number of winning squares. To determine if the particular square is winning you should do the following. Calculate the sum of all numbers on the squares that share this column (including the given square) and separately calculate the sum of all numbers on the squares that share this row (including the given square). A square is considered winning if the sum of the column numbers is strictly greater than the sum of the row numbers.
<image>
For instance, lets game was ended like is shown in the picture. Then the purple cell is winning, because the sum of its column numbers equals 8 + 3 + 6 + 7 = 24, sum of its row numbers equals 9 + 5 + 3 + 2 = 19, and 24 > 19.
Input
The first line contains an integer n (1 β€ n β€ 30). Each of the following n lines contain n space-separated integers. The j-th number on the i-th line represents the number on the square that belongs to the j-th column and the i-th row on the board. All number on the board are integers from 1 to 100.
Output
Print the single number β the number of the winning squares.
Examples
Input
1
1
Output
0
Input
2
1 2
3 4
Output
2
Input
4
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Output
6
Note
In the first example two upper squares are winning.
In the third example three left squares in the both middle rows are winning:
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Submitted Solution:
```
n=int(input())
row=[0]*n; col=[0]*n; count=0
for i in range(n):
l=list(map(int, input().split()))
row[i]+=sum(l)
for j in range(n):
col[j]+=l[j]
for i in range(n):
for j in range(n):
if row[i]<col[j]:
count+=1
print(count)
``` | instruction | 0 | 60,002 | 19 | 120,004 |
Yes | output | 1 | 60,002 | 19 | 120,005 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Sherlock Holmes and Dr. Watson played some game on a checkered board n Γ n in size. During the game they put numbers on the board's squares by some tricky rules we don't know. However, the game is now over and each square of the board contains exactly one number. To understand who has won, they need to count the number of winning squares. To determine if the particular square is winning you should do the following. Calculate the sum of all numbers on the squares that share this column (including the given square) and separately calculate the sum of all numbers on the squares that share this row (including the given square). A square is considered winning if the sum of the column numbers is strictly greater than the sum of the row numbers.
<image>
For instance, lets game was ended like is shown in the picture. Then the purple cell is winning, because the sum of its column numbers equals 8 + 3 + 6 + 7 = 24, sum of its row numbers equals 9 + 5 + 3 + 2 = 19, and 24 > 19.
Input
The first line contains an integer n (1 β€ n β€ 30). Each of the following n lines contain n space-separated integers. The j-th number on the i-th line represents the number on the square that belongs to the j-th column and the i-th row on the board. All number on the board are integers from 1 to 100.
Output
Print the single number β the number of the winning squares.
Examples
Input
1
1
Output
0
Input
2
1 2
3 4
Output
2
Input
4
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Output
6
Note
In the first example two upper squares are winning.
In the third example three left squares in the both middle rows are winning:
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Submitted Solution:
```
import sys
f = sys.stdin
#f = open("input.txt", "r")
n = int(f.readline().strip())
a = [list(map(int, i.split())) for i in f.read().split("\n")]
hs = []
for i in a:
hs.append(sum(i))
vs = []
for i in range(n):
s = 0
for j in range(n):
s += a[j][i]
vs.append(s)
cnt = 0
for i in hs:
for j in vs:
if j>i:
cnt += 1
print(cnt)
``` | instruction | 0 | 60,003 | 19 | 120,006 |
No | output | 1 | 60,003 | 19 | 120,007 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Sherlock Holmes and Dr. Watson played some game on a checkered board n Γ n in size. During the game they put numbers on the board's squares by some tricky rules we don't know. However, the game is now over and each square of the board contains exactly one number. To understand who has won, they need to count the number of winning squares. To determine if the particular square is winning you should do the following. Calculate the sum of all numbers on the squares that share this column (including the given square) and separately calculate the sum of all numbers on the squares that share this row (including the given square). A square is considered winning if the sum of the column numbers is strictly greater than the sum of the row numbers.
<image>
For instance, lets game was ended like is shown in the picture. Then the purple cell is winning, because the sum of its column numbers equals 8 + 3 + 6 + 7 = 24, sum of its row numbers equals 9 + 5 + 3 + 2 = 19, and 24 > 19.
Input
The first line contains an integer n (1 β€ n β€ 30). Each of the following n lines contain n space-separated integers. The j-th number on the i-th line represents the number on the square that belongs to the j-th column and the i-th row on the board. All number on the board are integers from 1 to 100.
Output
Print the single number β the number of the winning squares.
Examples
Input
1
1
Output
0
Input
2
1 2
3 4
Output
2
Input
4
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Output
6
Note
In the first example two upper squares are winning.
In the third example three left squares in the both middle rows are winning:
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Submitted Solution:
```
import math
def solve():
n=int(input())
#s#=input()
#n,b=map(int,input().split())
##m=int(input())
#l=list(map(int,input().split()))
#l1=list(map(int,input().split()))
#zero=s.count('0')
res=[]
for i in range(n):
l=list(map(int,input().split()))
res.append(l)
r=[0]*n
for i in range(n):
summ=0
for j in range(n):
summ+=res[i][j]
r[i]=summ
#print(r)
c=[0]*n
for i in range(n):
summ=0
for j in range(n):
summ+=res[j][i]
c[i]=summ
ans=0
for i in range(n):
for j in range(n):
if(c[i]>r[i]):
ans+=1
print(ans)
t=1
#t=int(input())
for i in range(t):
solve()
``` | instruction | 0 | 60,004 | 19 | 120,008 |
No | output | 1 | 60,004 | 19 | 120,009 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Sherlock Holmes and Dr. Watson played some game on a checkered board n Γ n in size. During the game they put numbers on the board's squares by some tricky rules we don't know. However, the game is now over and each square of the board contains exactly one number. To understand who has won, they need to count the number of winning squares. To determine if the particular square is winning you should do the following. Calculate the sum of all numbers on the squares that share this column (including the given square) and separately calculate the sum of all numbers on the squares that share this row (including the given square). A square is considered winning if the sum of the column numbers is strictly greater than the sum of the row numbers.
<image>
For instance, lets game was ended like is shown in the picture. Then the purple cell is winning, because the sum of its column numbers equals 8 + 3 + 6 + 7 = 24, sum of its row numbers equals 9 + 5 + 3 + 2 = 19, and 24 > 19.
Input
The first line contains an integer n (1 β€ n β€ 30). Each of the following n lines contain n space-separated integers. The j-th number on the i-th line represents the number on the square that belongs to the j-th column and the i-th row on the board. All number on the board are integers from 1 to 100.
Output
Print the single number β the number of the winning squares.
Examples
Input
1
1
Output
0
Input
2
1 2
3 4
Output
2
Input
4
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Output
6
Note
In the first example two upper squares are winning.
In the third example three left squares in the both middle rows are winning:
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Submitted Solution:
```
from sys import stdin,stdout
stdin.readline
def mp(): return list(map(int, stdin.readline().strip().split()))
def it():return int(stdin.readline().strip())
from pprint import pprint
n=it()
v=[]
for i in range(n):
v+= [mp()]
x = [[[0,0] for i in range(n)] for j in range(n)]
for i in range(n):
for j in range(n):
for k in range(n):
x[i][j][1] += v[i][k]
x[i][j][0] += v[k][j]
ans = 0
for i in range(n):
for j in range(n):
if x[i][j][1] > x[i][j][0]:
ans += 1
print(ans)
``` | instruction | 0 | 60,005 | 19 | 120,010 |
No | output | 1 | 60,005 | 19 | 120,011 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Sherlock Holmes and Dr. Watson played some game on a checkered board n Γ n in size. During the game they put numbers on the board's squares by some tricky rules we don't know. However, the game is now over and each square of the board contains exactly one number. To understand who has won, they need to count the number of winning squares. To determine if the particular square is winning you should do the following. Calculate the sum of all numbers on the squares that share this column (including the given square) and separately calculate the sum of all numbers on the squares that share this row (including the given square). A square is considered winning if the sum of the column numbers is strictly greater than the sum of the row numbers.
<image>
For instance, lets game was ended like is shown in the picture. Then the purple cell is winning, because the sum of its column numbers equals 8 + 3 + 6 + 7 = 24, sum of its row numbers equals 9 + 5 + 3 + 2 = 19, and 24 > 19.
Input
The first line contains an integer n (1 β€ n β€ 30). Each of the following n lines contain n space-separated integers. The j-th number on the i-th line represents the number on the square that belongs to the j-th column and the i-th row on the board. All number on the board are integers from 1 to 100.
Output
Print the single number β the number of the winning squares.
Examples
Input
1
1
Output
0
Input
2
1 2
3 4
Output
2
Input
4
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Output
6
Note
In the first example two upper squares are winning.
In the third example three left squares in the both middle rows are winning:
5 7 8 4
9 5 3 2
1 6 6 4
9 5 7 3
Submitted Solution:
```
n=int(input())
if n==1:
c=int(input())
print("0")
else:
arr=[]
row_sum=[]
col_sum=[]
for i in range(n):
a=list(map(int,input().split()))
arr.append(a)
row_sum.append(sum(a))
k=0
for i in range(n):
c=0
for j in range(n):
c+=arr[j][k]
k+=1
col_sum.append(c)
col_sum.sort()
count=0
for i in range(n):
for j in range(n-1,-1,-1):
if row_sum[i]>col_sum[j]:
count+=j+1
break
else:
continue
print(count)
``` | instruction | 0 | 60,006 | 19 | 120,012 |
No | output | 1 | 60,006 | 19 | 120,013 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 β€ i β€ n) such that ai > 0 and an integer t (t β₯ 0) such that i + 2t β€ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 β€ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 β€ ai β€ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 β€ n β€ 300
The input limitations for getting 50 points are:
* 1 β€ n β€ 2000
The input limitations for getting 100 points are:
* 1 β€ n β€ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40 | instruction | 0 | 60,007 | 19 | 120,014 |
Tags: greedy
Correct Solution:
```
n=int(input())
x = list(map(int, input().split(" ")))
sum=0
for i in range(n-1):
t=1
while i+2*t<n:
t*=2
sum+=x[i]
x[i+t]+=x[i]
x[i]=0
print(sum)
``` | output | 1 | 60,007 | 19 | 120,015 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 β€ i β€ n) such that ai > 0 and an integer t (t β₯ 0) such that i + 2t β€ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 β€ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 β€ ai β€ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 β€ n β€ 300
The input limitations for getting 50 points are:
* 1 β€ n β€ 2000
The input limitations for getting 100 points are:
* 1 β€ n β€ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40 | instruction | 0 | 60,008 | 19 | 120,016 |
Tags: greedy
Correct Solution:
```
import math
n = int(input())
args = input().split(" ")
seq = []
for x in args:
seq.append(int(x))
move_numbers = 0
for i in range(n - 1):
move_numbers = move_numbers + seq[i]
t = int(math.log2(n - 1 - i))
seq[i + 2 ** t] = seq[i + 2 ** t] + seq[i]
seq[i] = 0
print(move_numbers)
``` | output | 1 | 60,008 | 19 | 120,017 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 β€ i β€ n) such that ai > 0 and an integer t (t β₯ 0) such that i + 2t β€ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 β€ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 β€ ai β€ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 β€ n β€ 300
The input limitations for getting 50 points are:
* 1 β€ n β€ 2000
The input limitations for getting 100 points are:
* 1 β€ n β€ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40 | instruction | 0 | 60,009 | 19 | 120,018 |
Tags: greedy
Correct Solution:
```
n = int(input())
daf2 = []
for i in range(n):
x = bin(i)[2:]
daf2.append(x.count('1'))
daf = list(map(int, input().split()))
for i in range(n-1):
total = 0
lim_bawah = i+1
lim_atas = n
for j in range(0, i+1):
total += min(daf2[i+1-j:n-j]) * daf[j]
print(total)
``` | output | 1 | 60,009 | 19 | 120,019 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 β€ i β€ n) such that ai > 0 and an integer t (t β₯ 0) such that i + 2t β€ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 β€ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 β€ ai β€ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 β€ n β€ 300
The input limitations for getting 50 points are:
* 1 β€ n β€ 2000
The input limitations for getting 100 points are:
* 1 β€ n β€ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40 | instruction | 0 | 60,010 | 19 | 120,020 |
Tags: greedy
Correct Solution:
```
from collections import deque, defaultdict, Counter
from itertools import product, groupby, permutations, combinations, accumulate
from math import gcd, floor, inf, log2, sqrt, log10
from bisect import bisect_right, bisect_left
from statistics import mode
from string import ascii_uppercase
power_of_two = lambda number: int(log2(number))
num = int(input())
arr = list(map(int, input().split()))
new_arr = arr[::]
for i, n in enumerate(arr[:-1], start=1):
t = power_of_two(num-i)
ind = i + 2**t -1
new_arr[ind] += new_arr[i-1]
presum = list(accumulate(new_arr))
presum.pop()
for i in presum:
print(i)
``` | output | 1 | 60,010 | 19 | 120,021 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 β€ i β€ n) such that ai > 0 and an integer t (t β₯ 0) such that i + 2t β€ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 β€ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 β€ ai β€ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 β€ n β€ 300
The input limitations for getting 50 points are:
* 1 β€ n β€ 2000
The input limitations for getting 100 points are:
* 1 β€ n β€ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40 | instruction | 0 | 60,011 | 19 | 120,022 |
Tags: greedy
Correct Solution:
```
import math
n = int(input())
a = [int(s) for s in input().split(' ')]
def calculate(mylist):
number_of_steps = []
length = len(mylist)
def getLastIndex(i,n):
t = int(math.log(n - i,2))
return i + 2 ** t
for i in range(1,n):
if(i == 1):
number_of_steps.append(mylist[0])
mylist[getLastIndex(1,length) - 1] += mylist[0]
else:
number_of_steps.append(number_of_steps[-1] + mylist[i-1])
mylist[getLastIndex(i,length) - 1] += mylist[i-1]
for i in number_of_steps:
print(i)
calculate(a)
``` | output | 1 | 60,011 | 19 | 120,023 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 β€ i β€ n) such that ai > 0 and an integer t (t β₯ 0) such that i + 2t β€ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 β€ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 β€ ai β€ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 β€ n β€ 300
The input limitations for getting 50 points are:
* 1 β€ n β€ 2000
The input limitations for getting 100 points are:
* 1 β€ n β€ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40 | instruction | 0 | 60,012 | 19 | 120,024 |
Tags: greedy
Correct Solution:
```
import math
n = int(input())
l = list(map(int, input().split()))
count = 0
for i in range(n - 1):
p = i + 2 ** math.floor(math.log2(n-(i+1)))
count += l[i]
l[p] += l[i]
print(count)
``` | output | 1 | 60,012 | 19 | 120,025 |
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